#to calculate rotations

[endofunktor]

All numbers are imaginary. Some are useful.

So, @lipshits-continuous (I like your blog very much!) was bringing to my attention someone who was, let's say, a little frustrated about having to learn "imaginary numbers". You know. They're not even real.

I don't want to write about that person specifically, I don't know them at all.

But.

My siblings in crisis.

There are no "real" numbers in this world. The act of counting is already an abstraction. If you have an apple and a pear, then counting them as two pieces of fruit is an act of forgetting all the properties that distinguish them and remembering only those that unite them. Same goes for two apples of course.

So the number 2 is already entirely imaginary. Made up. Nonsense.

This gets worse very quickly, by the way. You can't have negative apples! Sure, you can have positive fractions of apples, but I can assure you: Two halves of an apple do rarely make one apple, except when they are the two halves of the same apple. And even then: Having them cut up makes it impossible to rejoin them. Think about that.

Now you know where this is going, because let's talk about the so-called ""real"" numbers. Nasty little things. Have a look at the irrational numbers. First, there are comparatively tame irrationals: Algebraic numbers. These arise as roots of integer polynomials. You know, like our favorite, the square root of 2, the positive zero of X^2 - 2.

Did you know that the Pythagoreans believed that everything was in integer relation to each other. (For example: the lengths of a rectangular triangle could be 3-4-5, meanging one cathetus is 4/5, the other 3/5 the length of the hypotenuse.) And that when someone found out that sqrt(2) was indeed not in integer relation to, say, 1, they had him murdered? That didn't change the fact that they were wrong though. (This story is not true, of course, like all good stories. You could say: it is imaginary, but nonetheless an interesting tale to tell!)

And now, the non-algebraic, so called transcendent numbers. Like pi. We know (the abstract concept of) pi well enough to calculate the circumference of the observable universe up to the accuracy of a neutrino (or so they say, I'm not a physicist). We don't have to know it any better. We could quit at however many digits we know and that would be pi. Perfectly rational. Because if we are looking for """real""" numbers only, why should we ever even concern ourself with those nasty things?

Did you know that transcendent numbers make the vast majority of real line? Of course you do! Rationals are countable, integer polynomials are countable and thus are their roots. The real line is famously uncountable, so must be the transcendent numbers.

So. Our so called """"real"""" numbers are mostly non-precisely calculable numbers. (Arbitrarily precise, but not precise.)

Do you know what kind of numbers are used in electrical engineering? Me neither because I'm not an electrical engineer. That's right, complex numbers! Actual engineers have to actually work with the actually imaginary square roots of negative one.

Maybe Numbers aren't a thing of this world.

Maybe Abstraction is a thing of our worldview.

And maybe we can learn to cherish abstract math the way we learn to cherish abstract art: Not always a true representation of reality, but a thing of interest and beauty in itself.

[sanerontheinside]

speaking of PTerry tho idk if this was by design, but the really really cool thing about trolls being in a base four number system is the fact that they're probably automatically pretty chill (lol) with complex numbers

because if you multiply i's they cycle in powers of 4

i is √(-1)

i x i is (√(-1))^2 = -1

i x i x i is -1 x i = -i

i x i x i x i is (-1)(-1) = 1

and then i x i x i x i x i just restarts the cycle at i

I mean there's no guarantee that rock trolls are on speaking terms with complex numbers but seriously imagine coming back to the meat futures warehouse and seeing your buddy literally doing shit that only kings do, that's pretty fascinating

[turtlespancake]

me when i write a character who is prone to dooming themself and then they run off and doom themself. core traits are stubbornness and a willingness to disregard their own humanity gET BACK HERE IM NOT DONE WITH YOU

[lgbstims]

math lesbian stimboard for anon

sources

[wolfcat-hybrid]

Trying to do worldbuilding for a planet is very hard when you don't know anything about astronomy, physics, hard science in general, and haven't taken a math class in several years

I wanted the planet to be small but otherwise Earth-like but apparently a planet that small would not be dense enough to hold an atmosphere together unless it was real close to its sun and if I wanted it to be real close to its sun while still being habitable it'd have to be a red dwarf star and actually a planet that orbited a red dwarf star that close would probably be tidally locked and the colors would be all weird and wait, how old is the planet, what about the moon, fuck we gotta figure out the tectonic plates, how the fuck do THOSE work--

.

.

..if this were a spec bio or sci-fi setting these would be interesting topics im sure. But I'm trying to put together a HIGH FANTASY SETTING. These guys wouldn't even appreciate the work I'm doing here!! In their setting the sun is a deity who handles LEGAL MATTERS they don't CARE ABOUT THISSSS

[catilinas]

cic. att. 15.4.2 trans. e-pistulae / lucan, pharsalia 1.36-43 trans. a.s. kline

thinking about THIS. caesar as a tree cut down but still living. pompey as a tree still standing but dead. etc.

[phoebe-twiddle]

It's my birthday 🥳

[hydrodragons]

once i get wriothesley on his rerun it's over for y'all

[forthesanityofstorytellers]

WHG Prompt 3 - Wonder and Curiosity

Lyra is pretty sure she wouldn't have any visitors. She's wrong.

Taglist: @concealeddarkness13 @maple-writes @pied-piper-of-hamlet @pen-of-roses @ratracechronicler

------------------------------------

Lyra fidgeted in the room, staring out the windows that looked out below. She wasn’t fond of this part last time, and she wasn’t fond of it this time. She had no friends, no relations, nobody to bother with her at the moment. Even the Capitol seemed to want to leave her alone right now, so this part was just a waiting game for her.

To her surprise, there came a knock at the door.

She turned with a frown, watching it open to find a family of three standing there. A woman and two kids, one a scruffy-looking boy fixing her with a frown and another a girl that looked far too young to be facing the games. But that was most of them, in her opinion. She had a hard time registering ages out here, as she had learned different places had different rates of light-passages. Lyra probably looked young by their standards. But by her home’s standards she was well into her adulthood and had a time to go yet.

She glanced at them in confusion as they came in and the door closed, only faintly realizing after a moment that the girl was the one whose place she ‘took’. So the woman was likely her mother, and the boy her brother. The mother seemed caught between confused suspicion and intense gratitude, with the latter winning out.

“I…I don’t know why you went in her place,” she finally managed to say, walking up to her.

“She’s too young,” Lyra answered. “She deserves another year at life. Plus I know what it’s like to be put in a situation to do something you don’t want to do just because someone in authority over you said you have to.”

She startled into a backwards step when the mother rushed forward and wrapped Lyra in a tight hug. “Thank you for volunteering. I…Thank you.”

Lyra nodded. She smiled at the girl and kneeled down. “Remember little one; just because they tell you that you can’t have hope and wonder doesn’t mean you have to listen to them. There’s lots of things to explore out there, you know.” She glanced around for a moment before tugging at the bandana around her ears, just enough to free them. The girl’s eyes widened as she saw Lyra’s pointed tips, and for extra effect Lyra wiggled them a little as well.

She grinned as she saw wonder and curiosity enter the girl’s features, staring at her ear. “I have antlers and wings too,” Lyra whispered, then pressed a finger to her lips. “Shh, don’t tell anyone.”

She slipped her ear back under the bandana carefully and stood, the mother turning back to her after glancing around. She took a small strip of cloth and tied it around Lyra wrist. “For luck. You’ll need it out there.”

Lyra nodded as the woman gathered up her kids and knocked to be let out, looking over the fabric. It was good quality. Nice. Had a bit of shine bordering the edges, something maybe designed to look like gold against the dark fabric. Lyra toyed with it for a moment before nodding. Luck…she’d need it if she was going to do what she aimed to do…and also if she had any hope of finding that scroll before someone else got their hands on it.

[adobodemon]

New OEC album veredict

[dykebluejay]

i love having friends and family who just look bemused but supportive when i ramble about weird math

[the-physicality]

i don't even know what to say

i had a bad feeling about this game ever since i went to watch and it was on *m*z*n pr*me

what happened to the offense

what happened to the defense [what happened to the defense is that atlanta has one 3 point threat and apparently washington has 8?

monique i thought had a very good game

celeste did well

natasha mack again had good impact

honestly i thought we took better care of the ball tonight than we have in a while but the shots were just not falling

i'm still annoyed at nate's rotations and honestly i think they are fucking up the first quarters

like i get that he's working on rotations or what ever but if people are getting points [the first points, the only points so far] maybe keep those people in instead of pulling them halfway through the quarter

i want to say this politely: it seems like he has pre planned rotations that he's going to implement regardless of the context of the game -_-

like we lost the 1st by 9, we lost the 2nd by 9, we lost the 3rd by 4 and we won the 4th by 9. thus the game by 13

if we lose the 1st by 5 instead that means that we've either played better defense or scored more points which keeps us hotter going into the 2nd, making it easier to play well, etc.

[sillywitchsong]

I'm 🤣. Apparently I only have 1 nice sim...(teen or older) and family was a distant third option...Haven't decided if I'm going to mess with changing the Tinyleaf second generation aspirations...but my game is about to get MESSY...all romance sims. All.

[fis-paprikas]

I am going. To start biting.

[anantaru]

ENTANGLEMENTS — ALHAITHAM

alhaitham hates working more than he has to but atleast he's got you to help him in a special way. wc. 600

・✶ ｡ warnings — cockwarming, office sex, petnames: princess, slightly dom alhaitham ??, fem! reader

"ugh, what a mess, this will take me hours to finish," alhaitham hisses lowly, gritting his teeth as his hands grab your hips to keep you in place— most importantly so you won't suddenly lose balance and fall off his lap as his cock throbs and twists in you, "—cannot wait to finish this and go home, princess,"

in natural response to his sugarlike spelling, your lips move close to his ear as you pant out a breathy moan of his name— crowded by his erection when his cock pushes against one particular searing spot, grazing against your sensitivity as his dick molds along your walls and stretches your hole good enough that you were hardly capable to think straight.

"now, what's that?" alhaitham chuckles— well, it sounded more like a strained snicker. although his eyes were sharp, nothing special, calculative and the scribe didn't miss your eyes rolling back into your skull now that your pussy grew accustomed to such fullness, your body eager awaiting to have him move himself in and out.

he averts his eyes from the piece of paper on his desk before roughly squeezing the flesh of your ass, making it jiggle under his large palms and adding in a subtle smack.

"keep quiet, remember there's people outside." you can only nod at him, both hands squeezing his strong shoulders before you force yourself to focus on the inviting sight of your boyfriend— his tight shirt lazily draped up, resting right under his chest and exposing his defined abs glistening with sweat, or his large hands pushing your hips down while not daring to drag himself out even once.

"you can take it, no?" he hums, "would be quite the shame if you didn't, don't you think? considering everything, in this moment you couldn't choose between what you found worse— the aching stretch of his thick shaft splitting you in half, although not moving, or the way how alhaitham was seemingly so unfazed by all of it, nonchalant as he rotates between toying with the plump flesh of your ass and focusing back on the important document resting on the table.

it was infuriating— but that's how the scribe was, and he always counted on your sweet pussy to wrap around him like second skin whenever he found himself borderline bored by his work.

your forehead falls flat to dig into his shoulder as you flutter awfully hard around his shaft, suddenly catching him inattentive as you triumph over your boyfriend just this once— his cheeks now flushing in the prettiest shade of pink when he notices the clench of your sore cunt, his eyes snapping shut and his lips parting flawlessly, his throat exposing an unplanned moan.

a blissed-out countenance accentuates his handsome face, tears stinging the corners of his soft lashes before he leans his head back.

"hah—," you chuckle breathlessly, your mind entirely clouded by just how amazing his cock felt in you, "you can take it, no?" you mimic his previous taunting, adding a slightly higher pitch as to get your point across, "would be quite— ah, fuck, fuck!" your jaw drops in awe as he snaps his hips upwards to fuck into you, chuckling as he gave your ass a light slap.

your toes curl when he pushes at a deep spot, satisfying stuns of lust surging throughout your abdomen and straight to your quivering pussy as alhaitham brings one hand to your chin, forcing your gaze to focus on his own famished glare.

"—easy now, what have i always told you about acting out like that? or disturbing my work, hm?"

©2024 anantaru do not repost, copy, translate, modify, claim as your own

[nasa]

Navigating Deep Space by Starlight

On August 6, 1967, astrophysicist Jocelyn Bell Burnell noticed a blip in her radio telescope data. And then another. Eventually, Bell Burnell figured out that these blips, or pulses, were not from people or machines.

The blips were constant. There was something in space that was pulsing in a regular pattern, and Bell Burnell figured out that it was a pulsar: a rapidly spinning neutron star emitting beams of light. Neutron stars are superdense objects created when a massive star dies. Not only are they dense, but neutron stars can also spin really fast! Every star we observe spins, and due to a property called angular momentum, as a collapsing star gets smaller and denser, it spins faster. It’s like how ice skaters spin faster as they bring their arms closer to their bodies and make the space that they take up smaller.

The pulses of light coming from these whirling stars are like the beacons spinning at the tops of lighthouses that help sailors safely approach the shore. As the pulsar spins, beams of radio waves (and other types of light) are swept out into the universe with each turn. The light appears and disappears from our view each time the star rotates.

After decades of studying pulsars, astronomers wondered—could they serve as cosmic beacons to help future space explorers navigate the universe? To see if it could work, scientists needed to do some testing!

First, it was important to gather more data. NASA’s NICER, or Neutron star Interior Composition Explorer, is a telescope that was installed aboard the International Space Station in 2017. Its goal is to find out things about neutron stars like their sizes and densities, using an array of 56 special X-ray concentrators and sensitive detectors to capture and measure pulsars’ light.

But how can we use these X-ray pulses as navigational tools? Enter SEXTANT, or Station Explorer for X-ray Timing and Navigation Technology. If NICER was your phone, SEXTANT would be like an app on it.  

During the first few years of NICER’s observations, SEXTANT created an on-board navigation system using NICER’s pulsar data. It worked by measuring the consistent timing between each pulsar’s pulses to map a set of cosmic beacons.

When calculating position or location, extremely accurate timekeeping is essential. We usually rely on atomic clocks, which use the predictable fluctuations of atoms to tick away the seconds. These atomic clocks can be located on the ground or in space, like the ones on GPS satellites. However, our GPS system only works on or close to Earth, and onboard atomic clocks can be expensive and heavy. Using pulsar observations instead could give us free and reliable “clocks” for navigation. During its experiment, SEXTANT was able to successfully determine the space station’s orbital position!

We can calculate distances using the time taken for a signal to travel between two objects to determine a spacecraft’s approximate location relative to those objects. However, we would need to observe more pulsars to pinpoint a more exact location of a spacecraft. As SEXTANT gathered signals from multiple pulsars, it could more accurately derive its position in space.

So, imagine you are an astronaut on a lengthy journey to the outer solar system. You could use the technology developed by SEXTANT to help plot your course. Since pulsars are reliable and consistent in their spins, you wouldn’t need Wi-Fi or cell service to figure out where you were in relation to your destination. The pulsar-based navigation data could even help you figure out your ETA!

None of these missions or experiments would be possible without Jocelyn Bell Burnell’s keen eye for an odd spot in her radio data decades ago, which set the stage for the idea to use spinning neutron stars as a celestial GPS. Her contribution to the field of astrophysics laid the groundwork for research benefitting the people of the future, who yearn to sail amongst the stars.  

Keep up with the latest NICER news by following NASA Universe on X and Facebook and check out the mission’s website. For more on space navigation, follow @NASASCaN on X or visit NASA’s Space Communications and Navigation website.  

Make sure to follow us on Tumblr for your regular dose of space!